Extract the information from big data with randomly distributed noise

Abstract In this manuscript, a purely data-driven statistical regularization method is proposed for extracting the information from big data with randomly distributed noise. Since variance of noise may be large, can regarded as general preprocessing in ill-posed problems, which able to overcome difficulty that traditional unable solve, and has superior advantage computing efficiency. The unique solvability proved, number conditions are given characterize solution. parameter strategy discussed, rigorous upper bound estimation confidence interval error L 2 L^{2} norm established. Some numerical examples provided illustrate appropriateness effectiveness method.